Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.18 . Each independently constructed a confidence interval based on the point estimate, but Jaime's interval has a lower bound of 0.107 and an upper bound of 0.194 , while Mariya's interval has a lower bound of 0.118 and an upper bound of 0.242 . Which interval is wrong? Why?
Choose the correct answer below.
A. Jaime's interval is wrong because it is too narrow
B. Mariya's interval is wrong because it is too wide.
C. Mariya's interval is wrong because it does not include the point estimate,
D. Jaime's interval is wrong because it is not centered on the point estimate
Answer
Final Answer: Jaime's interval is wrong because it is not centered on the point estimate. Therefore, the answer is \(\boxed{\text{D. Jaime's interval is wrong because it is not centered on the point estimate}}\)
Step 1 ：Define the intervals: Jaime's interval is [0.107, 0.194] and Mariya's interval is [0.118, 0.242].
Step 2 ：Calculate the middle point for each interval: Jaime's middle point is 0.1505 and Mariya's middle point is 0.18.
Step 3 ：Define the point estimate: The point estimate is 0.18.
Step 4 ：Check if the point estimate is the middle point of the intervals: The middle point of Jaime's interval is not equal to the point estimate, but the middle point of Mariya's interval is equal to the point estimate.
Step 5 ：Final Answer: Jaime's interval is wrong because it is not centered on the point estimate. Therefore, the answer is \(\boxed{\text{D. Jaime's interval is wrong because it is not centered on the point estimate}}\)
